Intuitionistic Fixed Point Theories for Strictly Positive Operators | Zendy

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Intuitionistic Fixed Point Theories for Strictly Positive Operators

Author(s) -

Rüede Christian,

Strahm Thomas

Publication year - 2002

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/1521-3870(200202)48:2<195::aid-malq195>3.0.co;2-s

Subject(s) - mathematics , iterated function , fixed point , fixed point theorem , operator (biology) , set (abstract data type) , discrete mathematics , point (geometry) , pure mathematics , algebra over a field , arithmetic , mathematical analysis , computer science , biochemistry , chemistry , geometry , repressor , transcription factor , gene , programming language

In this paper it is shown that the intuitionistic .xed point theory $ \widehat {\rm ID} ^{i} _{\alpha} $ (strict) for α times iterated fixed points of strictly positive operator forms is conservative for negative arithmetic and $ \Pi ^{0} _{2} $ sentences over the theory $ {\rm ACE} ^{-i} _{\alpha} $ for α times iterated arithmetic comprehension without set parameters.This generalizes results previously due to Buchholz [5] and Arai [2].

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